Government says 35 members of armed Islamist group died during shootout in predominantly Muslim northern city.

Nigerian forces have killed 35 suspected Boko Haram members in a crackdown on the insurgent group in the northeastern city of Damaturu, the country's military says.

"The Joint Task Force has succeeded in killing 35 Boko Haram terrorists in shootouts between Sunday evening through Monday," said Lieutenant Lazarus Eli, a military spokesman in Yobe state, of which Damaturu is the capital.

A round-the-clock curfew was imposed in the city late on Saturday, ahead of the operation that also led to the arrest of 60 suspected Boko Haram members.

The curfew has been relaxed and residents are now allowed out of their homes from 7:00am to 10:00pm, Eli said. The ban on movements in Yobe's economic capital of Potiskum has also been eased.

Military forces went door-to-door through three Damaturu neighbourhoods beginning late on Sunday and engaged militants in "a fierce exchange of gunfire" through to the early hours of Monday morning, the spokesman added in a statement.

Two soldiers were injured in the fighting.

Blamed for 1,400 deaths

Damaturu has been hit hard by the Islamist group which is blamed for more than 1,400 deaths in Africa's most populous nation since 2010.

Running gun battles between suspected Boko Haram members and the security forces in June put the city under lockdown, with some stranded in their places of work for several days unable to access food and water.

A list of weapons that Eli said were recovered from Boko Haram hideouts included dozens of guns, explosive devices and hundreds of rounds of ammunition, as well 32 arrows and two swords, among other items.

Analysts have said the group has purchased arms from markets in neighbouring Niger and has secured some of the weapons that poured out of Libya following the North African country's civil war.

Violence blamed on Boko Haram had ebbed in recent weeks, but a suicide blast at a church in the northern city of Bauchi on Sunday which killed a woman and a child resembled attacks previously claimed by the group.

Back-channel talks

Nigeria's military said that last week it had killed the man who has claimed such attacks on behalf of the group, when it shot dead a reported Boko Haram spokesman who used the alias Abul Qaqa outside the city of Kano.

Amid an apparent crackdown on the group's strongholds, Nigeria has said it is engaging in back-channel talks in an effort to halt the violence.

A previous attempt at dialogue this year collapsed when a mediator quit over leaks to the media.

Three of Boko Haram's leaders have been declared global terrorists by the US, but Washington has resisted calls to slap a terrorism designation on the entire organisation on the grounds that Boko Haram's primary focus is domestic.

US officials also say what has come to be known as Boko Haram may in fact be a number of different factions or groups.

Its main Islamist faction has said it wants to create an Islamic state in the north, but its demands have varied widely.